(3) Let [0 A = 1 [2 -2 2 3-2 4 -3 (a) Solve for the eigenvalues of A. (b) For each eigenvalue of A find a corresponding eigenvector.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
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(3) Let
[0
A = 1
2
-2 2
3-2
4 -3
(a) Solve for the eigenvalues of A.
(b) For each eigenvalue of A find a corresponding eigenvector.
(4) Consider the differential equation Dx = Ax where
[1 1 01
A = 1 1 0
[1 1 0]
(a) Find the general solution x of Dx = Ax.
(b) Find the unique solution such that
x(0) = 4
.
Transcribed Image Text:(3) Let [0 A = 1 2 -2 2 3-2 4 -3 (a) Solve for the eigenvalues of A. (b) For each eigenvalue of A find a corresponding eigenvector. (4) Consider the differential equation Dx = Ax where [1 1 01 A = 1 1 0 [1 1 0] (a) Find the general solution x of Dx = Ax. (b) Find the unique solution such that x(0) = 4 .
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